7.1 Integral As Net Change. Net Change Theorem If f’(x) is a rate of change, then the net change of f(x) over the interval [a,b] is This tells us the.

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Presentation transcript:

7.1 Integral As Net Change

Net Change Theorem If f’(x) is a rate of change, then the net change of f(x) over the interval [a,b] is This tells us the change that takes place in f(x) over the interval. Note: net change of a position function is called displacement.

Example Given that a particle in motion on the horizontal axis has a velocity given by, find the displacement after 5 seconds.

Example If assuming that in the previous example the particle had an initial position of s(0)=9, find the particles position after 1 second.

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Example A pump connected to a generator operates at a varying rate, depending on how much power is being drawn from the generator to operate other machinery. If the rate (gallons per minute) at which the pump operates was how many gallons were pumped in the first 10 minutes.

Total distance traveled To find the total distance traveled on an interval [a,b]: You may use a calculator to perform this integral.

Example In the same example we looked at earlier, we had Find the total distance that the object traveled in the first five seconds.

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Homework Pg 386 #1-5, 21, 22